Riemannian geometry and geometric analysis Jürgen Jost. Universitext.

From the reviews of the first and second editions: "... a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. ... The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references" Mathematical Rezensions " ...the tensorial and intrinsic methods are not separated in the discussions. Instead, the easiest to handle is used for the proofs. ...this symbiosis of these methods gives a deeper understanding for clever readers. ... The book develops the subjects very systematically and takes it beyond the standard introductory topics successfully. I recommend it to everybody, who is already acquainted with Riemannian Geometry, but wants to know it better and deeper or is interested in further nice investigations. Acta Scientarium Mathematicarum.